# JEE Main

Explore popular questions from Dual Nature of Matter and Radiation for JEE Main. This collection covers Dual Nature of Matter and Radiation previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Dual Nature of Matter and Radiation

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Q 1. If a source of power {tex} 4 \mathrm { kW } {/tex} produces {tex} 10 ^ { 20 } {/tex} photons/second, the radiation belongs to a part of the spectrum called

A

{tex} \gamma {/tex} -rays

{tex} \mathrm { X } {/tex} -rays

C

ultraviolet rays

D

microwaves

##### Explanation

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Q 2. Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is {tex} V _ { 0 } {/tex} and the maximum kinetic energy of the photoelectrons is {tex} K _ { \max } . {/tex} When the ultraviolet light is replaced by X-rays, both {tex} V _ { 0 } {/tex} and {tex} K _ { \max } {/tex} increase.
Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

Statement-1 is true, Statement-2 is false.

B

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-I.

C

Statement-l is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

D

Statement-1 is false, Statement-2 is true.

##### Explanation

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Q 3. Sodium and copper have work functions {tex} 2.3 \mathrm { eV } {/tex} and {tex} 4.5 \mathrm { eV } {/tex} respectively. Then the ratio of the wavelengths is nearest to

A

1:2

B

4:1

2:1

D

1:4

##### Explanation

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Q 4. Threshold wavelength for a metal having work function {tex}W_0{/tex} is {tex}X{/tex}. What is the threshold wavelength for the metal having work function {tex}2W_0{/tex}?

A

{tex}4\lambda{/tex}

B

{tex}2\lambda{/tex}

{tex}\frac{\lambda}{2}{/tex}

D

{tex}\frac{\lambda}{4}{/tex}

##### Explanation

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Q 5. Radiations of frequency {tex}v{/tex} are incident on a photosensitive metal. The maximum K.E. of the photoelectrons is {tex}E{/tex}. When the frequency of the incident radiation is doubled, what is the maximum kinetic energy of the photoelectrons?

A

{tex}2E{/tex}

B

{tex}4E{/tex}

{tex}E + hv{/tex}

D

{tex}E – hv{/tex}

##### Explanation

Using Einstein’s photoelectric equation {tex}hv – \phi = E{/tex}

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Q 6. The work function of a substance is {tex} 4.0 \mathrm { eV } . {/tex} The longest wavelength of light that can cause photoclectron emission from this substance is approximately

A

{tex} 540 \mathrm { nm } {/tex}

B

{tex} 400 \mathrm { nm } {/tex}

{tex} 310 \mathrm { nm } {/tex}

D

{tex} 220 \mathrm { nm } {/tex}

##### Explanation

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Q 7. Two identical photocathodes receive light of frequencies {tex} f _ { 1 } {/tex} and {tex} f _ { 2 } {/tex}. If the velocities of the photoelectrons (of mass {tex} m ) {/tex} coming out are respectively {tex} v _ { 1 } {/tex} and {tex} v _ { 2 } , {/tex} then

{tex} v _ { 1 } ^ { 2 } - v _ { 2 } ^ { 2 } = \frac { 2 h } { m } \left( f _ { 1 } - f _ { 2 } \right) {/tex}

B

{tex} v _ { 1 } + v _ { 2 } = \left[ \frac { 2 h } { m } \left( f _ { 1 } + f _ { 2 } \right) \right] ^ { \frac { 1 } { 2 } } {/tex}

C

{tex} v _ { 1 } ^ { 2 } + v _ { 2 } ^ { 2 } = \frac { 2 h } { m } \left( f _ { 1 } + f _ { 2 } \right) {/tex}

D

{tex} v _ { 1 } - v _ { 2 } = \left[ \frac { 2 h } { m } \left( f _ { 1 } - f _ { 2 } \right) \right] ^ { \frac { 1 } { 2 } } {/tex}

##### Explanation

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Q 8. According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal {tex} v s {/tex} the frequency, of the incident radiation gives a straight line whose slope

A

depends on the nature of the metal used

B

depends on the intensity of the radiation

C

depends both on the intensity of the radiation and the metal used

is the same for all metals and independent of the intensity of the radiation.

##### Explanation

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Q 9. The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

A

{tex} 540 \mathrm { nm } {/tex}

B

{tex} 400 \mathrm { nm } {/tex}

{tex} 310 \mathrm { nm } {/tex}

D

{tex} 220 \mathrm { nm} {/tex}

##### Explanation

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Q 10. A charged oil drop is suspended in a uniform field of {tex} 3 \times 10 ^ { 4 } \mathrm { V } / \mathrm { m } {/tex} so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge = 9.9 X 10 {tex}^ { - 15 } {/tex} kg and g = 10 m/s{tex} ^ { 2 }{/tex})

{tex} 3.3 \times 10 ^ { - 18 } \mathrm { C } {/tex}

B

{tex} 3.2 \times 10 ^ { - 18 } \mathrm { C } {/tex}

C

{tex} 1.6 \times 10 ^ { - 18 } \mathrm { C } {/tex}

D

{tex} 4.8 \times 10 ^ { - 18 } \mathrm { C } {/tex}

##### Explanation

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Q 11. If the kinetic energy of a free electron doubles, its de Broglie wavelength changes by the factor

{tex} 1 / \sqrt { 2 } {/tex}

B

{tex} \sqrt { 2 } {/tex}

C

{tex} 1 / 2 {/tex}

D

{tex} \mathrm 2{/tex}

##### Explanation

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Q 12. The time by a photoelectron to come out after the photon strikes is approximately

A

{tex} 10 ^ { - 1 } \mathrm { s } {/tex}

B

{tex} 10 ^ { - 4 } \mathrm { s } {/tex}

{tex} 10 ^ { - 10 } \mathrm { s } {/tex}

D

{tex} 10 ^ { - 16 } \mathrm { s } {/tex}

##### Explanation

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Q 13. The threshold frequency for a metallic surface corresponds to an energy of {tex} 6.2 \mathrm { eV } , {/tex} and the stopping potential for a radiation incident on this surface {tex} 5 \mathrm { V } {/tex}. The incident radiation lies in

A

X-ray region

ultra-violet region

C

infra-red region

D

visible region.